The parameter x0 defines the initial value of the underlying stochastic process.

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The parameter theta is the speed of mean-reversion. The parameter mu is the long-running mean. The parameter sigma is the volatility. In general, theta, mu, and sigma can be any algebraic expressions. However, if the process is to be simulated, these parameters must be assigned numeric values.

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The scheme option specifies the discretization scheme used for simulation of this process. By default the standard Euler scheme is used. When scheme is set to unbiased the transition density will be used to simulate a value X&ApplyFunction;t&plus;dt given X&ApplyFunction;t.

Compatibility

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The Finance[OrnsteinUhlenbeckProcess] command was introduced in Maple 15.